.. sounds like teething. Sometimes teething symptoms occurs before the teeth is actually coming up. Try looking it up online... I once read something like that.
If teething, it does cause a baby to feed not as well....but KEEP offering, on demand. They need a certain intake amount daily.
Or, it could be that he is sick. OR, it could be "Thrush"... try looking in his mouth, and if there are white "patches"...it can be Thrush. This also causes discomfort when feeding.
Teething discomfort varies with each baby, and each baby has different thresholds of tolerance to it. It may also cause him to not sleep as well, and/or it wakes them more at night. So keep that in mind, and just offer him comfort, don't just let him cry. If they wake because of teething/illness/discomfort... they can't help it.
Since he is only 3 months old, ask your Pediatrician... as to what you can give him.
Sometimes, gently rubbing their gums can give them some solace... or letting him knaw on frozen washcloths that are dampened a bit. My kids liked that.
All babies teeth at different times, some early, some later.
He may just want the bottle now, because IF he is teething... it's easier to "suck" from a bottle than from breast (from a bottle it's just by gravity)... but make sure you don't "skip" breastfeeding (if that is what your routine is), because it can affect your milk production (lessening it) since breastfeeding output is determined by supply and demand. And you don't want to get engorged, potentially.
Just check with your Pediatrician.
All the best,
Susan